21 citations · 23 across the 10 of their papers we have counts for
11 papers
On the -analogue of Duhamel's principle
Mohammed Elamine Sebih, Serikbol Shaimardan, Irfan Ali
In this paper, we revisit the classical Duhamel's principle and provide a self-contained proof of this fundamental tool for linear evolution equations and systems of coupled equati…
On a fractional nonlinear Schrödinger equation with irregular coefficients. case: d<2s
Arshyn Altyby, Michael Ruzhansky, Mohammed Elamine Sebih +1
In the case when , where is the space dimension and is the fractional power of the Laplacian, we study the well-posedness for a cubic nonlinear Schrödinger equation (…
Sign-changing solutions for a Yamabe type problem
Mohamed Bekiri, Mohammed Elamine Sebih
In this paper, we investigate the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary. The exi…
Non-homogeneous problem for the fractional wave equation with irregular coefficients and data
Manel Bouguenna, Mohammed Elamine Sebih
In this paper, we consider the Cauchy problem for a non-homogeneous wave equation generated by the fractional Laplacian and involving different kinds of lower order terms. We allow…
Wave equations for the fractional Sturm-Liouville operator with singular coefficients
Michael Ruzhansky, Mohammed Elamine Sebih, Alibek Yeskermessuly
In this paper, we consider the wave equation for the fractional Sturm-Liouville operator with lower order terms and singular coefficients and data. We prove that the problem has a…
Fractional wave equation with irregular mass and dissipation
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mas…
Schrödinger equation with singular position dependent mass
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
We consider the Schrödinger equation with singular position dependent effective mass and prove that it is very weakly well posed. A uniqueness result is proved in an appropriate se…
Heat equation with singular thermal conductivity
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense.…
Tsunami propagation for singular topographies
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the v…
The heat equation with strongly singular potentials
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
In this paper, we consider the heat equation with strongly singular potentials and prove that it has a "very weak solution". Moreover, we show the uniqueness and consistency result…
Fractional Schrödinger Equation with singular potentials of higher-order
Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih +1
In this paper, the space-fractional Schrödinger equations with singular potentials are studied. Delta-like or even higher-order singularities are allowed. By using the regularising…